I hope this example helps with my question.

Marked in "yellow". The diagonal coefficients should be constant or as close as possible.

The condtion number for this matrix is 51.3.

2 views (last 30 days)

Show older comments

Hi all,

This problem has stumped me due to my insufficient mathematical knowledge.

I am looking to determining the number of rows or columns of a lower triangular matrix, maintaining constant diagonal coefficients, for the minimum condition number.

Please see the attached PDF which describes what I am trying to do.

The best I have come up with is to check 5 different matrices, each with its number of rows/columns (solved using the finite element method to determine the number of steps {rows/columns}). I have attached the MAT files for these values for each matrix.

I did this with the following code. I then compare it manually.

% Diagonal elements of the "a" calibration matrix.

a_pn_d=diag(aij,0);

% Maximum and minimum diagonal elements of the "a" calibration matrix.

a_pn_d_max=max(a_pn_d);

a_pn_d_min=min(a_pn_d);

% Ratio of the minimum to maximum diagonal elements of the "a" calibration

% matrix.

a_pn_d_R=a_pn_d_min/a_pn_d_max;

% Relative error of each row.

a_sum=sum(aij,2);

a_sd=a_sum./a_pn_d;

% Condition number with a p-norm of 1, for the "a" calibration matrix.

% https://blogs.mathworks.com/cleve/2017/07/17/what-is-the-condition-number-of-a-matrix/#a3219326-029f-4d0b-bf53-12917948c5f2

a_cond_1=cond(aij,1);

Is there a method to optimise this problem, looking for the number of steps (rows/columns) of a lower triangular matrix, while maintaining constant diagonal coefficients as well as the minimum condition number for the matrix?

I am open to any suggestions and/or assistance in this regard.

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!